Solvent fluctuations and viscosity-dependent rates of solution reactions in a regime indescribable by the transition state theory

An organic molecule isomerizes in viscous solvents when appropriate cavities are formed around it in the course of slow diffusive thermal fluctuations of solvent molecules. The isomerization occurs when fast twisting (vibrational) fluctuations around a bond get to have large amplitudes in such cavities. This situation can be described by the two-reaction-coordinate model of Sumi and Marcus originally proposed for electron transfer reactions. In fact, the rate constant derived from this model fits nicely to that observed for thermal Z→E isomerization of substituted azobenzenes and N-benzylideneanilines. The rate constant is influenced by slow speeds of diffusive motions of solvent molecules, whose relaxation time τ is usually proportional to the solvent viscosity η. It has a form of k = 1/(k_TST^?1+k_f^?1), where k_TST, independent of τ, represents the rate constant expected from the transition state theory (TST), while k_f ∝ τ^? with 0 < ≤ 1 represents the part controlled by solvent fluctuations. An analytic expression of for the isomerization reactions is given in terms of physical parameters underlying the reaction mechanism with cavity formation.

This rate-constant formula is a general one applicable widely also to other solution reactions, covering from the TST-validated regime for a small τ to the TST-invalidated one for a large τ. In the former, k approaches k_TST since k_f k_TST, while in the latter, k approaches k_f since k_f k_TST, becoming decreasing with a decrease in the typical speed (∝ τ^?1) of solvent fluctuations. The dependence of k ≈ k_f ∝ η^? in the non-TST regime has often been observed also in biological reactions such as enzymatic ones. In this case, it is not appropriate to say that reactions are controlled by slow speeds of solvent fluctuations, but we should rather say that enzymes utilize this situation, which has been called conformational gating, in the course of solvent-fluctuation-driven conformational fluctuations of proteins. It has important meanings in protein functions.